Search our library of Maths A Level questions

Top answers

Maths

A Level

Find the partial fraction decomposition of the expression: (4x^2 + x -64)/((x+2)(x-3)(x-4)).

The first step to solving this question is inputting our dummy variables, and laying out the question so we know what we're doing.
So we end up with:(4x² + x - 64)/((x+2)(x-3)(x-4)) =

Answered by Matt V. • Maths tutor

3004 Views

Given f(x): 2x^4 + ax^3 - 6x^2 + 10x - 84, and knowing 3 is a root of f(x), which is the value of a?

For this exercise we need to be aware of the factor theorem.The factor theorem states when f(c) = 0 then x - c is a factor of the polynomial f(x) and c is a root of f(x). Because we are told that one of t...

Answered by Sabela R. • Maths tutor

2650 Views

A particle is in equilibrium under the action of four horizontal forces of magnitudes 5 newtons acting vertically upwards ,8 newtons acting 30 degrees from the horizontal towards the left,P newtons acting vertically downwards and Q newtons acting to right

first of all we need the resolve the diagonal force into its horizontal and vertical components. Using trigonometry you can deduce that the horizontal component equates to 8Cos30 and the vertical componen...

Answered by Ali A. • Maths tutor

5176 Views

A cricket player is capable of throwing a ball at velocity v. Neglecting air resistance, what angle from the horizontal should they throw at to achieve maximum distance before contact with the ground? How far is that distance?

Assume angle of throw theta. Resolving vertical and horizontal components: Vvert=v.sin(theta) and Vhoriz=v.cos(theta).From 'suvat' equations, time to vertical stationary t=v/a. This must be doubled to fin...

Answered by Benjamin W. • Maths tutor

2726 Views

f(x) = e^(sin2x) , 0 ≤ x ≤ pi (a). Use calculus to find the coordinates of the turning points on the graph of y = f(x)

First, understand the concept of a turning point (zero gradient, implying first derivative is zero at the turning point)How do we differentiate exponentials ( if f(x) = e^g(x) then f'(x) = g'(x)*e^g(x) ) ...

Answered by Marco W. • Maths tutor

5420 Views